ABSTRACT We present a novel technique for cosmic microwave background (CMB) foreground subtraction based on the framework of blind source separation. Inspired by previous work incorporating local variation to generalized morphological component analysis (GMCA), we introduce hierarchical GMCA (HGMCA), a Bayesian hierarchical graphical model for source separation. We test our method on Nside = 256 simulated sky maps that include dust, synchrotron, free–free, and anomalous microwave emission, and show that HGMCA reduces foreground contamination by $25{{\ \rm per\ cent}}$ over GMCA in both the regions included and excluded by the Planck UT78 mask, decreases the error in the measurement of the CMB temperature power spectrum to the 0.02–0.03 per cent level at ℓ > 200 (and $\lt 0.26{{\ \rm per\ cent}}$ for all ℓ), and reduces correlation to all the foregrounds. We find equivalent or improved performance when compared to state-of-the-art internal linear combination type algorithms on these simulations, suggesting that HGMCA may be a competitive alternative to foreground separation techniques previously applied to observed CMB data. Additionally, we show that our performance does not suffer when we perturb model parameters or alter the CMB realization, which suggests that our algorithm generalizes well beyond our simplified simulations. Our results open a new avenue for constructing CMB maps through Bayesian hierarchical analysis.
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Testing for directionality in the Planck polarization and lensing data
In order to better analyse the polarization of the cosmic microwave background (CMB), which is dominated by emission from our Galaxy, we need tools that can detect residual foregrounds in cleaned CMB maps. Galactic foregrounds introduce statistical anisotropy and directionality to the polarization pseudo-vectors of the CMB, which can be investigated by using the $\mathcal {D}$ statistic of Bunn and Scott. This statistic is rapidly computable and capable of investigating a broad range of data products for directionality. We demonstrate the application of this statistic to detecting foregrounds in polarization maps by analysing the uncleaned Planck 2018 frequency maps. For the Planck 2018 CMB maps, we find no evidence for residual foreground contamination. In order to examine the sensitivity of the $\mathcal {D}$ statistic, we add a varying fraction of the polarized thermal dust and synchrotron foreground maps to the CMB maps and show the per cent-level foreground contamination that would be detected with 95 per cent confidence. We also demonstrate application of the $\mathcal {D}$ statistic to another data product by analysing the gradient of the minimum-variance CMB lensing potential map (i.e. the deflection angle) for directionality. We find no excess directionality in the lensing potential map when compared to the simulations provided by the Planck Collaboration.
more » « less- NSF-PAR ID:
- 10122787
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 490
- Issue:
- 3
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 3404-3413
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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